If #f(x) = [5x^2+10x+26]/sqrt(x)# how do you find #f '(x)#?

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Answer 1 · 2015-04-06T18:35:10

You could use the quotient rule, but I think it's easier to first rewrite the expression algebraically.

#f(x) = [5x^2+10x+26]/sqrt(x) = (5x^2)/x^(1/2) +(10x)/x^(1/2) +26/x^(1/2)#

#f(x) = 5x^(3/2) +10 x^(1/2) +26x^(-1/2)#

So the derivative is:

#f'(x) = 3/2 5x^(1/2) +1/2 10 x^(-1/2) + (-1)/2 26 x^(-3/2)#

#f'(x) = 15/2 x^(1/2) +5 x ^(-1/2) - 13 x^((-3)/2)#

Rewrite this algebraically (get a common denominator) if you wish.

Answer 2 · 2015-04-06T18:40:19

I would use the Quotient Rule:
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